Torque magnetometry of an amorphousalumina/strontium-titanate interface
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Tomarken, S. L., A. F. Young, S. W. Lee, R. G. Gordon, and R.
C. Ashoori. "Torque magnetometry of an amorphousalumina/strontium-titanate interface." Phys. Rev. B 90, 201113
(November 2014). © 2014 American Physical Society
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http://dx.doi.org/10.1103/PhysRevB.90.201113
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RAPID COMMUNICATIONS
PHYSICAL REVIEW B 90, 201113(R) (2014)
Torque magnetometry of an amorphous-alumina/strontium-titanate interface
S. L. Tomarken,1 A. F. Young,1 S. W. Lee,2,* R. G. Gordon,2 and R. C. Ashoori1,†
1
2
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
(Received 12 September 2014; revised manuscript received 31 October 2014; published 24 November 2014)
We report torque magnetometry measurements of an oxide heterostructure consisting of an amorphous Al2 O3
thin film grown on a crystalline SrTiO3 substrate (a-AO/STO) by atomic layer deposition. We find a torque
response that resembles previous studies of crystalline LaAlO3 /SrTiO3 (LAO/STO) heterointerfaces, consistent
with strongly anisotropic magnetic ordering in the plane of the interface. Unlike crystalline LAO, amorphous
Al2 O3 is nonpolar, indicating that planar magnetism at an oxide interface is possible without the strong internal
electric fields generated within the polarization catastrophe model. We discuss our results in the context of current
theoretical efforts to explain magnetism in crystalline LAO/STO.
DOI: 10.1103/PhysRevB.90.201113
PACS number(s): 75.70.Cn, 75.30.Gw, 75.47.Lx
The interfacial two-dimensional electron gas (2DEG) in
LaAlO3 /SrTiO3 (LAO/STO) heterostructures has attracted
intense experimental and theoretical attention due to the hope
of tailoring the properties of strongly correlated electrons via
confinement [1,2]. In particular, the polar catastrophe model
that is thought to underlie the existence of a conducting
two-dimensional interface may provide a path to creating
confined, high carrier density electron systems without the
need for chemical doping [3,4]. An amorphous Al2 O3 thin
film grown on a crystalline SrTiO3 substrate (a-AO/STO)
provides a useful comparison system for the role of the polar
catastrophe in LAO/STO: Chemically similar yet structurally
distinct, the a-AO/STO interface is nonpolar. Theoretical
explanations of properties common to both systems, then,
should be reconciled with the absence of the strong electric
fields generic to polar catastrophe models in a-AO/STO. For
example, similarly to LAO/STO, a-AO/STO interfaces show
finite electrical conductivity above a critical thickness [5].
However, the charge carrier densities are roughly one order
of magnitude lower in a-AO/STO than in LAO/STO, and the
charge transport can be permanently suppressed by oxygen
postannealing of the amorphous samples [5,6]. These disparate
observations allow a reconciliation of the apparent similarity:
While it is likely that oxygen vacancy doping contributes to
the charge transport in both systems, the polar electric fields in
LAO/STO appear to generate a higher charge carrier density
and more robust interfacial conduction.
Among the notable features of the LAO/STO interface
has been the observation of magnetism [7–15]. As neither
of the parent materials is magnetic, the magnetism appears to
be a new property generated by the electronic confinement.
Relatively little is known about the origin of the magnetism,
with several distinct theoretical proposals awaiting experimental testing. These proposals fall into two categories, being
based either on intrinsic properties of the 2DEG in the polar
catastrophe scenario [16,17] or on (extrinsic) defect states that
may or may not be related to the strong fields generated in
the polar interfaces [18–20]. Here, we show that magnetism
*
Present address: Department of Physics and Division of Energy
Systems Research, Ajou University, Suwon 443-749, Korea.
†
ashoori@mit.edu
1098-0121/2014/90(20)/201113(4)
qualitatively similar to that observed in LAO/STO interfaces is
also present in a-AO/STO heterostructures. Our results raise
the possibility that growth defects play a large role in the
observation of magnetism in LAO/STO.
Our measurement involves placing a heterostructure on the
end of a brass cantilever so that the interface is parallel to
the cantilever [Fig. 1(b) inset]. In the presence of an applied
magnetic field H the cantilever will experience a torque
τ = m × μ0 H. For a moment m which is in the plane of
the interface, the torque signal will be τ = μ0 m(H )H cos φ,
where φ is the angle between the applied magnetic field and
the axis perpendicular to the interface [Fig. 1(a) inset]. Such
a torque will deflect the cantilever, and this deflection can
be detected via the change in the cantilever’s capacitance
to a nearby conducting plane. We point out that torque
magnetometry is directly sensitive to the magnetic moment
parallel to the plane of the cantilever. Accordingly, we are
sensitive to planar magnetic contributions from both the
interface as well as the substrate. However, we find it unlikely
that magnetic contributions far from the interface would show
strong planar anisotropy. We note that torque measurements
performed on bare STO substrates in Ref. [11] showed no
signs of planar magnetism.
Our sample consists of amorphous alumina grown on a
single crystal STO substrate using an atomic layer deposition
technique described previously [5]. 5 nm of amorphous
alumina were grown on a TiO2 -terminated STO substrate
at 300 ◦ C using trimethylaluminum and H2 O as the aluminum precursor and oxygen source, respectively. The room
temperature electron density at the a-AO/STO interface was
3 × 1012 cm−2 (determined by Hall measurement). A 100 nm
thick aluminum loop was subsequently deposited around the
edge of the 6 mm × 6 mm sample [see Fig. 1(b) inset] to allow
in situ calibration of the cantilever torque constant. The loop
was grounded when measuring the heterostructure torque. The
sample was fixed with GE varnish to a cantilever made from
25 μm thick brass foil. The cantilever was suspended on a
glass post above a fixed brass conducting plane on a G10 chip
carrier.
We measured capacitance with a 5 V excitation at 8 kHz
using a General Radio 1615A capacitance bridge and lock-in
amplifier. Measurements were performed with the sample
immersed in liquid 3 He (for base temperature measurements)
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FIG. 1. (Color online) Torque signal for different angles. (a) Small φ. The torque traces increase in amplitude monotonically with increasing
angle |φ|. The torque traces invert about φ = 0◦ . Inset: Schematic depicting the interface and applied field. (b) Large φ. For φ > 27◦ , the
torque signal monotonically decreases with increasing φ. The torque traces are proportional to H⊥ = H cos φ. As φ approaches 90◦ , the torque
amplitude vanishes. Inset: Picture of a brass cantilever with the sample. The dark ring around the sample is a calibration loop.
or 3 He gas (for the high temperature measurements in Fig. 3).
The magnetic field was ramped at a constant rate of 0.3 T min−1
with no detectable hysteresis. We report data from one
sample with our most complete torque series and temperature
dependence. We also saw similar signs of magnetic ordering
in one other nominally identical sample.
Figure 1 shows torque traces for different interface orientations at 400 mK. The angle φ describes the tilt angle
of the magnetic field with respect to the axis perpendicular
to the interface [Fig. 1(a) inset]. For a constant in-plane
moment m(H ) = m0 , the torque signal is linear in H .
For a more general in-plane moment m(H ) which evolves
as a function of the applied field, the torque traces will
be nonlinear at low applied field but will reach a linear
regime once the in-plane moment has saturated (as in a
superparamagnetic or ferromagnetic system). In addition to
a possible linear signal indicative of magnetic ordering, the
sample may also have an overall paramagnetic or diamagnetic
background. Although torque of the form m × μ0 H vanishes
for paramagnetic and diamagnetic contributions (m ∝ H), the
presence of small magnetic field gradients perpendicular to
the plane of the cantilever results in a deflection proportional
to ∇ (m · μ0 H). For paramagnetic or diamagnetic moments
(m ∝ H) this corresponds to a deflection proportional to
H 2 . At low applied field we are dominated by the linear
deflection response, which we interpret (following Ref. [11])
as arising from in-plane magnetic ordering. We restrict our
range to |μ0 H | < 0.5 T to remain within this regime. (See
Fig. 3 for an example of a larger field range with quadratic
contributions.)
Figure 1(a) shows torque traces for small φ. At φ ≈ 0◦
there is a negligible torque signal, indicating the absence
of an in-plane magnetic moment. As the angle is tilted in
either the positive or negative direction, the torque signals
monotonically increase in magnitude with the sign of the
slope determined by the tilt direction. The slope inversion
about φ = 0◦ suggests that, as in LAO/STO [11], there is
either no coercive field or one that cannot be resolved with our
technique, which loses sensitivity at small applied field. The
increase in torque signal indicates an increase of the in-plane
moment up to a maximum value which occurs between
about |φ| ≈ 10◦ and 25◦ . At applied field H 0.25 T, the
torque traces are linear, indicating a constant in-plane moment
consistent with either superparamagnetism or ferromagnetism
with a small coercive field which we cannot detect. We note
that the size of the in-plane moment in the linear regime shows
dependence on the out-of-plane field (see Fig. 2). This is
consistent with a picture of the interfacial moments canting
slightly out of the plane of the interface when subjected to a
strong out-of-plane field. However, because our measurement
is only sensitive to the in-plane field, we have no way of
verifying this picture and make no claims as to the origin
of this dependence. Figure 1(b) shows torque traces at larger
tilt angles. After passing through a maximum at φ = 27◦ , the
torque signal monotonically decreases as φ approaches 90◦ ,
where the applied field is parallel to the interface. Because
τ ∝ H⊥ , the torque signal is strongly suppressed at large
angles and vanishes completely at φ = 90◦ .
The angle between the applied field and the interface
was determined by first setting the interface perpendicular
to the applied magnetic field (φ = 0◦ ). This was achieved
by both observing a torque trace with zero amplitude as
well as a maximum in the cantilever to conducting plane
capacitance. Our cryogenic rotation stage was controlled by
a room temperature calibrated linear actuator. By referencing
the position of the linear actuator relative to φ = 0◦ we could
determine the angle of inclination of the rotation stage with
respect to the applied field. However, this does not take into
account the mechanical bending of the cantilever as the rotation
stage changes orientation. This may cause an error in our angle
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FIG. 2. (Color online) Magnetic moment calculation. The magnetic moment m(H ) was calculated from the torque traces by dividing
by the perpendicular applied field: m(H ) = τ (H )/μ0 H cos θ. The
trace corresponding to φ = 90◦ was excluded due to the loss of
sensitivity around φ ∼ 90◦ . Data below 50 mT have been suppressed
due to loss of torque sensitivity at low field. The net magnetic moment
has been expressed in units of Bohr magnetons μB per 2D STO unit
cell (u.c.).
calibration by as much as 5◦ –10◦ , particularly at large angles.
However, we stress that this calibration does not affect the
essential results of our measurement.
Comparison of the torque data in Fig. 1 with Fig. 4 from
Ref. [11] shows that our data is in qualitative agreement
with previous results from crystalline LAO/STO. However,
the torque signal from a-AO/STO is roughly one order of
magnitude stronger than that observed in Ref. [11] despite
a similar sample size, indicating a much higher net in-plane
moment in the amorphous system. We can calculate the size of
the in-plane magnetic moment through the relation m(H ) =
τ (H )/(H cos φ). Figure 2 shows m(H ) traces calculated from
selected torque traces in Fig. 1. The magnetic moment has
been expressed in units of the Bohr magneton and normalized
by the number of 2D unit cells (u.c.) in one layer of crystalline
STO. Note that this normalization corresponds to the effective
areal moment density, as if all of the signal were confined
to the interface. Although we do not know the true spatial
distribution of the magnetic moments, this convention allows
comparison of our experimental data to theories making
quantitative predictions of local moments within the first
interfacial TiO2 layer as well as a direct comparison to
Ref. [11]. Explicit computation of τ (H )/(μ0 H cos φ) within
the |μ0 H | < 50 mT range has been suppressed due to the loss
of torque sensitivity at low field. We have also excluded the
trace corresponding to φ = 90◦ due to loss of torque sensitivity
when the applied field is parallel to the interface. The
FIG. 3. (Color online) Temperature dependence of torque.
Torque traces at constant φ = −11◦ from 400 mK to 30 K. There
is no quantitative change in torque signal below 0.5 T throughout
the accessible temperature range. The curvature at the higher field is
due to an overall diamagnetic background.
in-plane moment achieves a maximum of 5–8μB /2D u.c. in
this particular sample and is roughly one order of magnitude
larger than the 0.3–0.4μB /2D u.c. estimate of crystalline
LAO/STO in Li et al. [11] (see Fig. 1(d) in Ref. [11]).
However, the large moment density makes it unlikely that the
magnetic signal arises from a truly two-dimensional layer at
the interface. The magnetic moments are likely distributed in
a three-dimensional volume within the STO. Lacking another
obvious mechanism to explain the magnetic anisotropy, we
suspect the magnetic moments are near the interface.
We also measured the temperature dependence of the
magnetism. In Fig. 3 we plot the torque τ (H ) traces at
constant tilt angle φ = −11◦ from 400 mK up to 30 K, the
highest temperature achievable in the 3 He cryostat. There is
no quantitative change in the torque signals below 0.5 T (the
regime most sensitive to magnetic ordering). The curvature
in the torque traces at a higher applied field is due to the
overall diamagnetic background of the sample and shows a
weak temperature dependence. Li et al. [11] found a similar
lack of temperature dependence up to 40 K (see Fig. 3 in
Ref. [11]).
Our amorphous sample demonstrates magnetic ordering
with strong planar anisotropy, no detectable coercive field,
and stability at elevated temperatures—in striking similarity
with results from crystalline LAO/STO. However, our estimate
of 5–8μB /2D u.c. differs quantitatively from the magnetic
moment estimate of 0.3–0.4μB /2D u.c. found in Ref. [11].
Because the a-AO/STO interfaces should have a much smaller
electric polarization than crystalline LAO/STO, yet show a
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PHYSICAL REVIEW B 90, 201113(R) (2014)
much larger areal moment density, our data raise the possibility
that growth defects are largely responsible for magnetic
ordering in both epitaxial and amorphous oxide interfaces
which have not been oxygen postannealed.
In addition to considering previous torque measurements,
our results may provide an important context for recent reports
of interfacial magnetism in LAO/STO. We note that Ref. [15]
found evidence of the absence of interfacial magnetism in
oxygen postannealed LAO/STO heterostructures using x-ray
absorption spectroscopy. The residual magnetism observed in
oxygen annealed samples [15] was consistent with previous
neutron reflectometry results [13]. However, Ref. [14] found
evidence of Ti3+ magnetism in oxygen annealed samples.
It has also been recently proposed that the polarization
catastrophe may generate interfacial defects which ultimately
are responsible for localized magnetic moments at the interface
[20]. In this scenario Ti-on-Al antisite defects are responsible for magnetism and not oxygen vacancies, as proposed
elsewhere [18]. Our data do not rule out the possibility of
distinct mechanisms driving qualitatively similar magnetism
in epitaxial LAO/STO and a-AO/STO. Rather, our results
point to the necessity of incorporating the role of growth
related defects when describing interfacial magnetism in
oxides.
There are several future measurements that could isolate
which aspects of the oxide interface landscape are responsible
for magnetism. Namely, performing similar torque measurements on oxygen annealed samples could demonstrate
whether or not the magnetism arises from oxygen vacancies.
Similarly, performing magnetometry on a-AO/STO structures
with different overlayer thicknesses (especially near the 1.5 nm
critical thickness) could reveal to what degree (if any) the
magnetism is influenced by the presence of a 2DEG. However,
as in the crystalline system, isolation of the role of oxygen
vacancies from electronic reconstructions remains a challenge.
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This work was sponsored by the BES Program of the
Office of Science of the U.S. DOE, Contract No. FG0208ER46514, and the Gordon and Betty Moore Foundation,
through Grant No. GBMF2931. This material is based upon
work supported by the National Science Foundation Graduate
Research Fellowship under Grant No. 1122374. A portion
of this work was performed at the National High Magnetic
Field Laboratory, which is supported by National Science
Foundation Cooperative Agreement No. DMR-1157490, the
State of Florida, and the U.S. Department of Energy. A.F.Y.
acknowledges the support of the MIT Pappalardo Fellowship
in Physics.
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